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A064190 Triangle T(n,k) generalizing the tangent numbers. 2

%I

%S 1,2,6,16,48,72,272,816,1440,1440,7936,23808,44352,57600,43200,353792,

%T 1061376,2027520,2903040,3024000,1814400,22368256,67104768,129964032,

%U 195379200,232243200,203212800,101606400,1903757312,5711271936

%N Triangle T(n,k) generalizing the tangent numbers.

%H J. L. Arregui, <a href="http://arXiv.org/abs/math.NT/0109108">Tangent and Bernoulli numbers</a> related to Motzkin and Catalan numbers by means of numerical triangles.

%F T(n+1, m) = m*(m+1)*Sum_{k = m-1, n} T(n, k)

%e 1; 2,6; 16,48,72; 272,816,1440,1440; ...

%t t[1, 1] = 1; t[1, 0] = 0; t[n_ /; n > 1, m_] := t[n, m] = m*(m+1)*Sum[t[n-1, k], {k, m-1, n-1}]; Table[t[n, k], {n, 1, 8}, {k, 1, n}] // Flatten (* _Jean-Fran├žois Alcover_, Jan 02 2013 *)

%Y First column gives A000182.

%Y If m*(m+1) is replaced in the formula by m*m, the first column is the sequence of secant numbers A000364. - Jose L. Arregui (arregui(AT)posta.unizar.es), Oct 09 2001

%K nonn,tabl,easy,nice

%O 0,2

%A _N. J. A. Sloane_, Sep 21 2001

%E More terms from _Vladeta Jovovic_, Sep 22 2001

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Last modified February 23 17:41 EST 2018. Contains 299584 sequences. (Running on oeis4.)